(4Z-3)(7+Z)=0

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Solution for (4Z-3)(7+Z)=0 equation:


Simplifying
(4Z + -3)(7 + Z) = 0

Reorder the terms:
(-3 + 4Z)(7 + Z) = 0

Multiply (-3 + 4Z) * (7 + Z)
(-3(7 + Z) + 4Z * (7 + Z)) = 0
((7 * -3 + Z * -3) + 4Z * (7 + Z)) = 0
((-21 + -3Z) + 4Z * (7 + Z)) = 0
(-21 + -3Z + (7 * 4Z + Z * 4Z)) = 0
(-21 + -3Z + (28Z + 4Z2)) = 0

Combine like terms: -3Z + 28Z = 25Z
(-21 + 25Z + 4Z2) = 0

Solving
-21 + 25Z + 4Z2 = 0

Solving for variable 'Z'.

Factor a trinomial.
(-7 + -1Z)(3 + -4Z) = 0

Subproblem 1

Set the factor '(-7 + -1Z)' equal to zero and attempt to solve: Simplifying -7 + -1Z = 0 Solving -7 + -1Z = 0 Move all terms containing Z to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1Z = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1Z = 0 + 7 -1Z = 0 + 7 Combine like terms: 0 + 7 = 7 -1Z = 7 Divide each side by '-1'. Z = -7 Simplifying Z = -7

Subproblem 2

Set the factor '(3 + -4Z)' equal to zero and attempt to solve: Simplifying 3 + -4Z = 0 Solving 3 + -4Z = 0 Move all terms containing Z to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4Z = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4Z = 0 + -3 -4Z = 0 + -3 Combine like terms: 0 + -3 = -3 -4Z = -3 Divide each side by '-4'. Z = 0.75 Simplifying Z = 0.75

Solution

Z = {-7, 0.75}

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